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Please excuse the long-winded nature of my response; my collaborator Dave Parks
who among other abilities has knife-edge editing skills, is on a long trip to
Madagascar, doing field biology and taking LOTS of photos. Look for his slide
show at the next ISAC!
I) Log amp transfer functions
To refresh everyone's memory, the graphs Tom constructed were made by
evaluating the ratio of two beads with different fluorescence intensities as
they are scanned accross the range of the log amp by varying the PMT voltage.
This results in a plot of mean channel number of the bead pair on the x-axis
and bead peak difference on the y-axis.
This graph, however, is NOT the transfer function of the log amp. (We described
how to construct that in our 1988 ISAC poster from data similar to this).
Rather, thie data reperesents the derivative of the transfer function; it shows
the change in effective channels/decade of the log amp as a fuction of signal
level. Since log amps are not ideal devices, the graph will fluctuate over the
full signal range. The y-axis channel difference is not directly convertable to
mV of signal (as Tom tried to do); rather it can be scaled to channels/decade.
The formula is:
ch/dec = (mean bead diff)/log(bead ratio)
In the case of Tom's data, he showed a mean bead difference of 11 channels out
of 256 for a bead ratio of 1.69, which results in 48.2 ch/decade, or about 5.3
decades if the amp performed this way over the entire scale.
Graphs like this we have found very useful for adjusting our log amps to put
the best log characteristic where the most relevant immunoflurescent data is,
from the second to the fourth decade. Then first decade data mainly represent
the autofluorescence of lymphocytes.
II) Digitization resolution
One consideration here is accuracy of measurement - it makes no sense to
digitize at a resolution more accurate than the analog electronics as a whole,
or underlying biology. For a four-decade log amp, digitization at 512 channels
yields a channel-to-channel difference of about 2% in signal level (8 bits
yields about 3.6%.for 4 decade amp, 10 bits is about .9%). However, the ADC's
have inaccuracies in them as well, so we genrally digitize at a higher
resolution, then throw away the least significant bits, storing at least 9 bits
of data for computation.
III) Smoothing
Data smoothing is not a solution to elctronics problems such as digitization
jitter or switching transients. These result from either poor circuit design or
component failure and should be attended to.
Our measurements show that lymphocyte autofluorescence is about 2 to 20 times
the intesity of "noise" (this depends on where in the spectrum it is measured)-
"noise" being at least the sum of laser noise, electronic noise, and PMT dark
current. Thus the channel-to-channel difference of signals above autoflurescence
in the second to the fourth decades is minimally due to this "noise" level
imposed upon the signal. Measurement conditions, such as the cell's position in
the jet or dye quenching, will have a greater effect.
Thus, variations in data taken on a cell sample are due to "sampling",
in a statistical sense, rather than electronic measurement error. 1 and 2-d
histograms are an approximation of the underlying distribution and will appear
quite ragged if the number of events measured is "small". Taking more data is
an obvious method of getting "smoother" graphs, because the sampling variation
is reduced. However, for analytic purposes (population parameters such as
means, % of total, etc), one can get quite accurate results without a "smooth"
approximation to the underlying distribution. Smoothing algorithms are
appropriate to make the data visually more understandable without having to
spend inordinate amounts of time collecting large data sets.
In our software system we use a smoothing algorithm whose parameters have been
adjusted to make the plots of a 10K data set appear as if they were computed
from a 100K data set. Most of our users find this to be very helpful when
viewing 2-d contour plots.
IV) Conclusions (general)
For immunofluorescent data, make sure your log amps are adjusted properly, take
at least 9 bit data for accurate computations, and smooth graphical output for
ease of visualization.
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